Randomness and dimension in computational learning and analog computation

Abstract

Above all, I would like to thank my parents Elga and Nikolai, and the rest of my family as well, for their love and support.Ella, for your love, kindness, and companionship.Kevin, for always making me feel understood. Carlos and Nolan, for spending time with me in nature, under my broken car, and on the couch watching good movies instead of working. Emily for your friendship and kindness. Thank you all for reminding me that rest and fun are as much a part of my personal development as research is. Thank you for helping me persist from week to week, mentally and spiritually. Thank you for your friendship from the bottom of my heart.Mara, for your warmth, friendly face, and soft little paws. Christopher for your approving glare.My advisor Jack Lutz for everything it took to mentor me for six years -a great scientist and a kind and patient teacher. My other committee members James Lathrop, Pavan Aduri, Gianfranco Ciardo, Andrew Miner, and Tony Smith for their time, kindness, encouragement, and insights. Tony Smith, again, for being a patient and articulate philosophical interlocutor and teacher.Gopal Krishnasamy and Adam Case who played a direct role in sparking my interest in theory as an undergraduate.Nicole and Carla, and everyone else at Atanasoff hall and at Iowa State who keeps the lights on, floors clean, and affairs in order. Everyone intersecting my time in the Laboratory for Molecular Programming, including Xiaoyuan Li,